Selecting a separable parametric spatiotemporal covariance structure for longitudinal imaging data

Longitudinal imaging studies allow great insight into how the structure and function of a subject's internal anatomy changes over time. Unfortunately, the analysis of longitudinal imaging data is complicated by inherent spatial and temporal correlation: the temporal from the repeated measures and the spatial from the outcomes of interest being observed at multiple points in a patient's body. We propose the use of a linear model with a separable parametric spatiotemporal error structure for the analysis of repeated imaging data. The model makes use of spatial (exponential, spherical, and Matérn) and temporal (compound symmetric, autoregressive-1, Toeplitz, and unstructured) parametric correlation functions. A simulation study, inspired by a longitudinal cardiac imaging study on mitral regurgitation patients, compared different information criteria for selecting a particular separable parametric spatiotemporal correlation structure as well as the effects on types I and II error rates for inference on fixed effects when the specified model is incorrect. Information criteria were found to be highly accurate at choosing between separable parametric spatiotemporal correlation structures. Misspecification of the covariance structure was found to have the ability to inflate the type I error or have an overly conservative test size, which corresponded to decreased power. An example with clinical data is given illustrating how the covariance structure procedure can be performed in practice, as well as how covariance structure choice can change inferences about fixed effects.